# De utilitate mathematicae 140

Theon Smyrnaeus, De utilitate mathematicae, Paragraph 140. Ancient Greek.

Canonical: https://interlinea.aeterna-institute.org/library/greek/theon-smyrnaeus/de-utilitate-mathematicae/140

ὑπεναντία δὲ τῇ ἁρμονικῇ καλεῖται μεσότης, ὅταν ὡς ὁ τρίτος ὅρος πρὸς τὸν πρῶτον, οὕτως ἡ τοῦ πρώ- του ὑπεροχὴ πρὸς τὴν τοῦ δευτέρου· οἷον ςʹ εʹ γʹ· τὰ μὲν οὖν ςʹ τῶν εʹ μονάδι ὑπερέχει, τὰ δὲ εʹ τῶν γʹ δυσί· τὰ δὲ γʹ τῶν ςʹ ὑποδιπλάσιά ἐστιν· ἀλλὰ καὶ ἡ μονὰς ὑπεροχὴ οὖσα τοῦ [τε] πρώτου ἀριθμοῦ ὑποδιπλασία ἐστὶ τῆς δυάδος ὑπεροχῆς οὔσης τοῦ δευτέρου ἀριθμοῦ.

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Theon Smyrnaeus, De utilitate mathematicae, ed. Eduardus Hiller. Text: The Greek Library, from the Perseus Digital Library and other open sources, CC BY-SA 4.0. Changes: apostrophes normalised and the text divided into reading sections by Interlinea.
License: CC BY-SA 4.0 (https://creativecommons.org/licenses/by-sa/4.0/). Source: https://thegreeklibrary.pages.lisn.upsaclay.fr/works/tlg1724.tlg001.local001/.